{
  "id": "math/0612058",
  "version": "v1",
  "published": "2006-12-02T19:23:35.000Z",
  "updated": "2006-12-02T19:23:35.000Z",
  "title": "Plancherel-Rotach Asymptotics for $q$-Laguerre Orthogonal Polynomials with Complex Scaling",
  "authors": [
    "Ruiming Zhang"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CA",
    "math.CV"
  ],
  "abstract": "In this work we study the Plancherel-Rotach type asymptotics for $q$-Laguerre orthogonal polynomials with complex scaling . The main term of the asymptotics contains Ramanujan function $A_{q}(z)$ for the scaling parameter on the vertical line $\\Re(s)=2$, while the main term of the asymptotics involves the theta function for the scaling parameter in the strip $0<\\Re(s)<2$. In the latter case the number theoretical property of the scaling parameter completely determines the order of the error term. $ $These asymptotic formulas may provide insights to some new random matrix model and add a new link between special functions and number theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-02T19:23:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E15",
      "33D45"
    ],
    "keywords": [
      "laguerre orthogonal polynomials",
      "complex scaling",
      "plancherel-rotach asymptotics",
      "scaling parameter",
      "main term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12058Z"
    }
  }
}